The law regarding copyright is fairly simple: If you've created it then you own it. However, what you create must not contain creative content that has been produced by someone else who retains copyright. However, this must be in the context of originality.

If you go outside and film a bird flying in the sky, that piece of footage belongs to you, and nobody else can use it without your permission. If you add a soundtrack created by someone else then you must assure you have permission from the soundtrack artist before using it, and, in most cases, you will have to pay them a small royalty fee.

Note:
There is a large repository of public domain and free to use content (audio and visual) that can be utilized to avoid royalties, if your own creation is also free to use your will even expand the type of freely licensed source materials you can use.

You can film anywhere within the public domain without obtaining copyright permissions; however, if there is music being played and it is picked up in your recording then may be required obtain permission to use that music. Permission must be sought when filming on Private Land, National Trust areas, land owned by the Ministry of Defense and similar type areas.

Note:
The issue with copyright assumption is that the last major reform removed the requirement to specifically inform others about the copyright status of their creations, and so today all creative work must be assumed to be under copyright even if as time goes by the copyright works are a minority in regards to the ones that already reverted into the public domain.

Many people believe that if you are not making a profit from your video then you don't have to seek copyright permission. This is not true. You can be prosecuted regardless and whether or not you are making a profit. Profit only determines how much you are fined.

Note:
It is however safe to assume that works that generate profit are more likely to get into legal problems or infringe in (or provide competition to) the economic interests of others.

There are various different types of copyright such as Performing Artists Copyright which is when you are recording a live band and Master Recording Copyright which is when you want to dub in a particular piece of material (such as a CD) which source must not be altered or re-performed.